"As VCC falls below approximately 3.0V, a power switching circuit turns the internal lithium energy source on to maintain the
clock and timer data functionality. It is also required to ensure that during this time (battery-backup
mode), that the voltage present at INTA and INTB (INTB) never exceeds VBAT. During power-up, when
VCC rises above VBAT, the power-switching circuit connects external VCC and disconnects the internal
lithium energy source. Normal operation can resume after VCC exceeds 4.5V for a period of 200ms."
The above is from the ds1486-120 datasheet. I believe Vcc is normally around 5v so a circuit could be built that allows 4.2v to charge the external battery while the unit is on and then blocks the current to the rest of the board when the unit is off (when the external battery provides 3.7v to the chip). This would require the pin32 (Vcc) to be lifted and integrated with the simple battery circuit.
Can anyone say why this would not work?